Microlens arrays having high focusing efficiency

ABSTRACT

Microlens arrays ( 105 ) having high focusing efficiencies are provided. The high focusing efficiencies are achieved by accurately producing the individual microlenses making up the array at high fill factors. Arrays of positive microlenses are produced by forming a master having a concave surface-relief pattern ( 101 ) in a positive photoresist ( 21 ) using direct laser writing. Through this approach, the problems associated with the convolution of a finite laser beam with a desired profile for a microlens are overcome. The microlens arrays of the invention have focusing efficiencies of at least 75%.

CROSS REFERENCE TO RELATED PROVISIONAL APPLICATION

This application claims the benefit under 35 USC §119(e) of U.S.Provisional Application No. 60/222,032 filed Jul. 31, 2000, the contentof which in its entirety is hereby incorporated by reference.

I. FIELD OF THE INVENTION

The present invention relates to arrays of microlenses having highfocusing efficiencies. It also relates to methods for fabricating sucharrays.

The invention is applicable to the efficient focusing of laser lightinto optical fibers, light diffusion, and controlled scattering ofcoherent or incoherent light for projection and transmissive displays,among other applications.

II. DEFINITIONS

The following definitions are used herein:

A “microlens array” is an array of microlenses and an associated arrayof unit cells, with one microlens being associated with each unit cell.The microlenses of the present invention can have any desiredconfiguration and can be formed on, for example, a supporting “piston”of the type disclosed in commonly assigned U.S. patent application Ser.No. 60/222,033 which was filed on Jul. 31, 2000 in the names of G.Michael Morris and Tasso R. M. Sales and is entitled “Structured Screensor Controlled Spreading of Light,” the content of which in its entiretyis incorporated herein by reference. Thus, as used herein, the term“microlens” means any microstructure which is capable of focusing light.

The “fill factor” of a microlens array is the ratio of the sum of theareas within the unit cells occupied by microlenses to the sum of theareas of the unit cells.

The “focusing efficiency” of a microlens array is the sum of themeasured light intensities at the focal points of the microlensesdivided by the sum of the light intensities impinging on the unit cellsof the array for an array illuminated along its optical axis by acollimated, substantially spatially incoherent light source, e.g., acollimated white light source. As will be recognized by those skilled inthe art, this is a “Strehl-type” definition of focusing efficiency.

Since concave microlenses will typically have virtual focal points(e.g., a plano-concave microlens in air will have a negative power andthus a virtual focal point for collimated light), an auxiliary opticalsystem needs to be used in such cases to produce real focal points whoseintensities can be measured. To at least some extent, the auxiliaryoptical system will reduce the intensities at the real focal points, andthose reductions should be taken into account in determining theintensity values for the virtual focal points.

In the case of anamorphic microlenses, the light intensities at each ofthe focal points of the microlens are included in the sum of themeasured light intensities.

III. BACKGROUND OF THE INVENTION

Microlenses are required in many applications, such as light couplingfrom lasers to fibers, either as single lenses or in array form wherebyseveral beams are focused to several fibers. Other importantapplications include light diffusion and screens.

Depending on the application, one may require a microlens of accurateprofile with controlled focusing properties or, in the case of an array,high quality over most lenses in the array. To focus light efficiently,the lens profile (or sag function) must be fabricated with accuracytypically equal to or better than, for example, λ/4, where λ is thewavelength of the illumination source.

In addition, particularly for high-density coupling, diffusion, orscreen applications, it is often important that the microlenses utilizethe entire surface for focusing. In this way, essentially all incidentlight can be controlled by the array. When the entire useful surfacearea is employed for focusing, the array is said to possess a 100% fillfactor.

Close packing of microlenses implies a fill factor equal to 100%, whichmeans that the internal boundaries between neighboring microlenses arein close contact. A simple example of close packing is a hexagonalarray. Other arrangements, such as square arrays, can also be closepacked.

It is typical to find in both the scientific and patent literaturearrays of microlenses that have fill factors below 100%. FIG. 1illustrates such an array where microlenses 12 are regularly placed onthe available substrate area 11 with spaces being left between theindividual microlenses. One of the unit cells of the array of FIG. 1 isshown by dashed lines 13. The fill factor for this array is only 44%.

There are several existing methods for fabricating isolated microlensunits or arrays of microlenses whose edges are well-separated so thattheir boundaries avoid close contact. Because there is a finite distancebetween the internal boundaries of neighboring lenses, the fill factorfor the array is necessarily less than 1 (or 100%).

The difficulty in obtaining efficient closed-packed lens arrays usingprior art fabrication methods is due to the inability of those methodsto preserve the boundaries of microlenses accurately, particularly forsmall and strongly focusing lenses.

Methods using thermal deformation, such as that disclosed in U.S. Pat.No. 5,324,623, are based on volume relaxation and thus cannot controlthe fusing of material at the internal boundaries between microlenses.With fusion there is distortion that reduces focusing capabilities.Thermal deformation methods are simple to implement but allow limitedcontrol of the individual microlens structures.

Other methods, such as those described in U.S. Pat. No. 5,300,263,involve the creation of mechanical molds that define receptacles forcurable liquids. The liquid is poured into the receptacles and thenatural surface tension creates a bowed surface that serves as themicrolenses. The mold, with the various receptacles, defines the arrayarrangement. Due to the inherent limitation of this method incontrolling the shape of the microlens units, its efficiency cannot beoptimized for a general application. Other mechanical methods based onthe direct ruling of individual microlenses, such as diamond turning,are better suited for the fabrication of individual microlenses ratherthan arrays.

Methods based on ion diffusion processes that provide gradient-indexarrays, such as those described in U.S. Pat. No. 5,867,321, cannotprovide a 100% fill factor, with the region between two neighboringmicrolenses being typically 20% of the microlens repetition spacing.Gradient-index arrays present a serious limitation for large-volumefabrication due to the intrinsically slow diffusion process.

Processes for producing microlens arrays using direct laser writing in aphotoresist are known in the art. See commonly-assigned PCT PatentPublication No. WO 99/64929, Gale et al., U.S. Pat. No. 4,464,030, andMicro-Optics: Elements, systems and applications, Hans P. Herzig, ed.,Taylor & Francis, Bristol, Pa., 1997, pp. 53-152. The photoresist ofchoice for such processes is a positive photoresist since compared tonegative photoresists, positive photoresists are more widely available,have been subject to more intensive research and development work byphotoresist manufacturers, and generally have higher resolution.However, as discussed in detail below, prior to the present invention,it has not been possible to produce arrays of positive microlenseshaving high focusing efficiencies at high fill factors using positivephotoresists.

The present invention addresses the difficulties associated with theprior art by providing methods for fabricating microlens arrays havinghigh focusing efficiencies through accurate microlens fabrication athigh fill factors. The array can be arranged in any arbitrary way, suchas square, hexagonal, or random. In addition, the methods allow thefabrication of microlenses of arbitrary shape as well as variablefocusing power for different directions (anamorphic lenses).

IV. SUMMARY OF THE INVENTION

In view of the foregoing, the objects of the invention include at leastsome and preferably all of the following:

(1) the provision of fabrication methods for producing arrays of convexmicrolenses having high focusing efficiencies;

(2) the provision of arrays of convex and/or concave microlenses withgreater than 75% focusing efficiency, preferably greater than 85%focusing efficiency, and most preferably greater than 95% focusingefficiency;

(3) the provision of methods for accurately fabricating arrays of convexmicrolenses at high fill factors; and/or

(4) the provision of arrays of accurately fabricated convex and/orconcave microlenses with fill factors greater than 90%, preferablygreater than 95%, and most preferably approximately 100% so that theentire useful area of a substrate can be employed for focusing or, moregenerally, scattering of an illuminating beam.

In connection with these objects, it is also an object of the inventionto allow the microlenses of the array to have arbitrary shapes (sagfunctions) that can vary randomly within the array.

It is a further object of the invention to provide improved methods forusing positive photoresists to produce arrays of convex microlenses athigh fill factors.

To achieve the foregoing and other objects, the invention provides afabrication method for producing an array of convex microlenses whereindirect laser writing is used to produce an initial master (initial mold)in a positive photoresist wherein the surface configuration of theinitial master is the negative (complement) of the desired array ofconvex microlenses. That is, the initial master has a concave, insteadof a convex, surface configuration. In this way, as discussed in detailbelow, the problems caused by the finite size of a laser beam and theconvolution of such a beam with the desired profile(s) of convexmicrolenses are overcome. By overcoming these problems, convex microlensarrays having high focusing efficiencies are achieved.

In general, a high focusing efficiency for an array of microlensesdepends on two factors: (1) a high fill factor, and (2) accuratereproduction of the desired lens profiles. Both factors are necessaryand neither factor alone is sufficient.

Thus, a high fill factor can be achieved by a process that alters allparts of a resist film, but if the alterations do not correspond to thedesired lens profiles, the focusing efficiency of the array will stillsuffer since the parts of the resist film that have the inaccurateprofiles will not focus incident light properly. On the other hand,accurate reproduction of a desired lens profile with the individualmicrolenses spaced far apart also results in low focusing efficiency, inthis case as a result of light passing through the spaces betweenmicrolenses.

In accordance with the invention, it has been found that both factorscan be addressed by using the concave form to initially write convexlenses in a positive photoresist. In this way, high focusing efficiencythrough the accurate production of desired lens profiles at a high fillfactor is achieved.

In accordance with certain preferred embodiments, the invention ispracticed by using a substrate typically made of glass to support afirst medium to generate an initial master (initial mold), which islater used to accurately replicate the desired microlens array in acost-effective fashion. More particularly, a photosensitive positiveresist film is deposited on the substrate to an appropriate thicknessconsistent with the desired thickness for the final microlens array. Thepositive resist is preferably of the low-contrast kind such that, whenexposed to light, a smoothly varying surface-relief profile can beproduced.

After being deposited on the substrate, the positive resist is exposedto a laser beam having a well-characterized profile. With a pre-definedsampling rate, the area of the resist film of interest is exposed to thelaser beam. By varying the intensity of the beam, the complement of theshape of each microlens in the array is encoded in the resist. Inparticular, the laser exposure produces a latent image in thephotosensitive film by modifying its physical and chemical properties.

Next, the film is developed to produce a surface-relief structure. For aresist film of the positive kind, development removes the exposed arealeaving the unexposed regions. The above combinations of surface-reliefstructure and photoresist type for the initial master are criticalaspects of the invention since only through the indicated combinationscan high focusing efficiencies be achieved through high fill factors andminimized convolution effects of a finite laser beam.

It has been generally believed in the art that the convolution effectsof a finite laser beam would be essentially the same irrespective ofwhether the laser beam exposure created a convex or concavesurface-relief structure. In accordance with the invention, it has beenfound that this belief is not true and in fact by fabricating theinitial master for a convex microlens array as a concave surface-reliefstructure, high fill factors (e.g., fill factors equal to or essentiallyequal to 100%) and high focusing efficiencies (e.g., focusingefficiencies at least above 75%) are achieved. A detailed discussion ofhow this combination addresses the convolution problem is presentedbelow.

To create a mold usable in high volume replication, intermediaryreplication steps are generally necessary because resist films areusually unsuitable for large-volume replication. For example, theconcave surface-relief structure can be used to prepare an intermediatemaster (intermediate mold), which is of convex form. The intermediatemaster can then be replicated once more to provide a final master (finalmold), now in concave form. Large-volume replication is then possiblewith the final concave master so that the final array has a convex formand provides a high fill factor and a high focusing efficiency.

The array need not be limited to regularly periodic arrangements, suchas square or hexagonal arrays, but may assume any general arbitraryform, as dictated by the requirements of the design. Furthermore, thelens shape need not be the same and can, in fact, vary for everymicrolens in the array. For example, the techniques of the presentinvention can be used to produce the configurations and distributions ofmicrostructures set forth in the above-referenced, commonly assignedU.S. Patent Application entitled “Structured Screens for ControlledSpreading of Light.”

A fact of importance in the present invention is that the tops of theconcavities of the concave surface-relief structure formed in thepositive resist film are preferably aligned or vary slowly for anyneighboring elements. If this guideline is not satisfied, accurateprofiles may only be produced over a portion of the array, reducing boththe fill factor and the focusing efficiency of the array.

V. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of a lens array with a fill factor less than 100%.

FIG. 2 shows a glass substrate with a photosensitive film deposited onits surface.

FIG. 3 shows the scanning of a laser beam over a photosensitive filmcreating a region of distinct chemical properties (latent image).

FIG. 4A and FIG. 4B show the effect of convolution in the fabrication ofconvex structures.

FIG. 5A and FIG. 5B illustrate the interaction of a hard fabricationtool in relation to a convex and concave array, respectively.

FIG. 6 illustrates a technique for estimating the focusing efficiency ofthe microlens units of an array fabricated in convex form.

FIG. 7A and FIG. 7B show experimental plots of identical microlensprofiles fabricated in convex and concave forms, respectively.

FIG. 8 and FIG. 9 illustrate surface-relief structures having concavecavities formed in a positive photoresist where the edge boundaries ofthe cavities are aligned with the top surface of the photoresist.

FIG. 10A, FIG. 10B, and FIG. 10C illustrate the replication of aninitial mold having concave cavities to obtain a final array of convexmicrolenses.

VI. DETAILED DESCRIPTION OF THE INVENTION

Referring now to the figures, FIG. 2 shows a photosensitive resist film21 of low contrast deposited on a substrate 22 which is typically madeof glass. The thickness of the film should be equal to or larger thanthe total depth span defined by the lens array. Depending on the totalthickness of the array, the resist may require preliminary processingsuch as hardening.

After the initial resist processing, a laser beam is focused at theresist film and scanned along the surface so as to expose the wholeresist surface, as indicated in FIG. 3. The intensity of the laser beamvaries for every point in such a fashion that a latent image of thenegative of the desired convex microlenses is imprinted in the resist inthe form of a chemical transformation of the resist material.

To obtain a surface-relief structure the chemically modified resist filmundergoes a development process, which consists of exposure to asolution of, for example, a standard alkali developer for a period oftime that varies with the total thickness of the array. Deeper arraysrequire longer development times. For a resist of the positive type, thedevelopment process removes the exposed areas, leaving the unexposedareas.

According to the inventive process described herein, each microlens inthe array needs to be produced in the positive photoresist in concaveform. Only in this way is it possible to reduce significantly therounding effect observed when microlenses are fabricated in convex form.This is so because the fabrication process itself introduces featuresinto a surface-relief profile that are undesirable.

Given the mathematical description of the desired surface-reliefstructure and the writing laser beam, the relief structures obtained byexposure of a resist film are generally described as the convolution ofthe desired surface function with the laser beam function. The operationof convolution can be mathematically described by the followingrelation: $\begin{matrix}{{{F\left( {x,y} \right)} = {\int_{S}{\int{{f\left( {x^{\prime},y^{\prime}} \right)}{g\left( {{x^{\prime} - x},{y^{\prime} - y}} \right)}{x^{\prime}}{y^{\prime}}}}}},} & (1)\end{matrix}$

where f represents the mathematical function describing the desiredsurface relief, g represents the mathematical form of the writing laserbeam, S represents the fabricated surface area, (x,y) denotes a point onthe surface of the photosensitive film, and F represents the finalsurface shape.

The validity of Eq. (1) relies on the assumption that the interaction ofthe laser beam and the photosensitive film is linear, in the sense thatthe response of the film is in direct proportionality to the intensityof the laser exposure and that the superposition of several beams has asimple additive effect. To a good approximation this assumption iscorrect and can be observed in surface-relief structures fabricated inconvex form, that is, structures that protrude from the resist surfaceas illustrated in FIGS. 4A and 4B.

The fact that the expected convolution effects are readily observed inconvex structures has led to the general belief that the same type ofbehavior would happen for concave shapes. In fact, if one uses Eq. (1),and notes that to obtain the concave shape one simply needs to multiplythe convex shape by −1 and add a constant, then it would appear that thefinal shape should be the same for both the concave and the convexshapes, except for the change in sign.

However, it turns out that the interaction between the laser beam andthe photosensitive film is not linear and, therefore, the convolutionrelation can describe the fabrication process only approximately. Infact, in accordance with the invention, we have discovered that thelaser writing process is more akin to the fabrication of devices bymeans of hard mechanical apparatuses such as diamond tools.

In such fabrications, convolution effects are still present but they areof a different nature than those observed with a laser beam becauselatent image-formation is nonexistent and superposition effects do notoccur. It is the contact of the mechanical tool with the surface beingruled that creates the surface relief. There is, however, an intrinsicasymmetry in the mechanical fabrication of convex and concavestructures. Because of the finite size of the tool, it is not possibleto penetrate the narrow region between two neighboring structures, butthere is no difficulty in creating the sharp contact point of twoconcave structures. This is illustrated in FIGS. 5A and 5B.

In accordance with the invention, we have found that the laser writingprocess operates according to similar principles and exhibits similarasymmetry when considering convex and concave shapes. This surprisingresult enables the fabrication of fully-packed convex microlens arrays,as opposed to previous methods that can only guarantee accurate profilesover a fraction of the aperture of the array in a fully-packedarrangement.

Importantly, the laser-writing process when used to make concavesurface-relief structures not only achieves the advantage of mechanicalruling devices for concave structures but also offers significantcapabilities that go beyond those of mechanical ruling methods. Forinstance, there is virtually no limitation regarding the size or shapeof microlenses made with the laser-writing process. Also, the size ofthe mechanical tool itself determines the extent of the boundary regionbetween neighboring microlenses. With laser writing, this region can bearbitrarily reduced.

The ability to preserve a concave surface-relief shape from the apex ofthe structure to its very edge at the boundary of a neighboringconcavity allows for the fabrication of arrays of convex microlenses ofhigh focusing efficiency. It does so since it allows the final convexmicrolenses to have a fully-packed arrangement. In contrast, if thearray is directly produced in convex form, independent of whether oneuses a mechanical tool, a laser tool, or other process, the boundariesof two neighboring microlenses cannot be usefully employed for focusingand thus the array will have a reduced focusing efficiency.

This deficiency of producing an array in convex form, whether by meansof a mechanical or a laser tool, is illustrated in FIG. 6. In thisfigure, the desired microlens shape is represented by curve 61 with anarea available for focusing represented by the parameter A. However, dueto the fabrication, the actual microlens shape turns out be that givenby curve 62 and the area available for focusing now being represented bythe parameter B. The observed rounding effect at the boundaries of themicrolenses diverts the incident illumination to locations other thanthe focal point of the microlens. Therefore, only area B becomesavailable for focusing. In this way, the estimated focusing efficiencyof the microlens η can be written as $\begin{matrix}{\eta = {\left( \frac{B}{A} \right)^{2} \times 100{\%.}}} & (2)\end{matrix}$

With the prior art, B is always less than A so that the focusingefficiency is less than 100%. With the current inventive process, theinitial surface-relief structure is written in concave form so thatsharp boundaries between lenses are well reproduced in the finalmicrolens array. When the concave master is replicated one obtains aconvex array such that B essentially equals A. Consequently the focusingefficiency is essentially 100%.

Experimental studies have confirmed the above analysis, especially inthe case of convex microlenses of high numerical aperture (fast lenses)where light is focused at large angles. FIG. 7A shows the case of anarray of microlenses with diameter equal to 50 μm fabricated in convexmode. The boundaries between microlenses are clearly rounded and cannotbe efficiently used for focusing. The estimated efficiency for eachmicrolens in this array is 50%.

On the other hand, when the same array is fabricated in concave form oneobtains a far better result, as shown in FIG. 7B. Note that theboundaries are preserved. This array is estimated to be 100% efficientin focusing. In addition the concave surface-relief structure can befully packed without losing efficiency. Direct writing of a convex arraycannot achieve such packing without loss of efficiency.

As another important component of the present inventive process, theconcavities of the concave surface-relief structure formed in thepositive photoresist should have their extremities aligned with thesurface of the resist as indicated in FIG. 8. Any variations from thedesirable alignment should be slow enough so as to avoid excessiverounding of the ultimate microlenses that would lead to low transmissionefficiency. The analogy between the mechanical ruling and the laserwriting starts to fail when neighboring concavities present a relativevertical offset, such as, the “piston” of the above-referenced, commonlyassigned patent application entitled “Structured Screens for ControlledSpreading of Light.” For some types of screen applications, the reducedefficiency might be acceptable. In other cases, the loss in focusingefficiency is intolerable.

As shown in FIG. 9, the requirement of alignment between the top of theconcavities of the concave surface-relief structure is fully compatiblewith the requirement of some arrays that the focusing properties of theindividual microlenses vary randomly. In this case, the vertices of theconcavities do not align, only their tops. A similar principle appliesfor two dimensional arrays.

After development, the surface-relief structure obtained with the laserexposure provides a first mold that can be used for replication. If thematerial that constitutes the photosensitive film is suitable forreplication, than replicas of that master can be readily fabricated inconvex form. If concave replicas are required, an intermediatereplication step is necessary whereby a convex tool is formed, which isready to produce concave arrays. Typically, the photosensitive film isnot suitable for many replications and, as a result, molds arepreferably made of, for example, stronger plastic resins.

A representative replication process is illustrated by the sequenceshown in FIG. 10A through FIG. 10C.

FIG. 10A shows the initial surface-relief structure 101 in concave formwith the tops aligned. The substrate, e.g., glass substrate, isidentified by the reference number 102. FIG. 10B shows another substrate103 on which a plastic resin 104 has been deposited. This resin will beone more suitable than a photoresist for use or as an intermediatereplication tool. FIG. 10C shows the result of replication of theintermediate replication tool of FIG. 10B to generate the desired arrayof convex microlenses 105.

Sequences similar to that shown in FIG. 10 can be used to make highefficiency, high fill factor arrays of concave microlenses with againthe initial surface-relief structure being formed in a positivephotoresist in concave form.

Although specific embodiments of the invention have been described andillustrated, it will be apparent to those skilled in the art thatmodifications and variations can be made without departing from theinvention's spirit and scope. The following claims are thus intended tocover the specific embodiments set forth herein as well as suchmodifications, variations, and equivalents.

What is claimed is:
 1. A method for producing a microlens array, saidmicrolens array having a surface configuration having peaks and valleysand comprising a plurality of unit cells and a plurality of microlenses,one microlens per unit cell, said method comprising: (a) providing apositive photoresist; (b) exposing the positive photoresist with a laserbeam having a finite beam width at the photoresist of less than thetransverse size of any of the microlenses being formed, said exposingbeing performed using a direct laser writing process which employsrelative movement between the finite beam width of the laser beam andthe positive photoresist to form a latent image in the photoresist; (c)developing the latent image to form a photoresist master, saidphotoresist master having a surface configuration which is substantiallythe negative of the surface configuration of the microlens array; and(d) using the photoresist master to: (i) produce the microlens array,and/or (ii) produce a further master used to form the microlens array,said further master having a surface configuration which issubstantially the negative of the surface configuration of the microlensarray; wherein: (A) said microlens array comprises only convexmicrolenses at adjacent unit cells so that the photoresist master andthe further master if produced comprises only concavities at adjacentunit cells; (B) the microlens array has a focusing efficiency greaterthan 50 percent; and (C) the microlens array would have a focusingefficiency of 50 percent or less if prepared by the same direct laserwriting process using the same laser beam with the same finite beamwidth at the photoresist but with the photoresist master being writtenso as to comprise convexities at adjacent unit cells rather thanconcavities.
 2. The method of claim 1 wherein the photoresist masterlies between a first plane and a second plane, the concavities extendinto the photoresist master in the direction from the first planetowards the second plane, and the maximum sag of each concavity is atthe first plane.
 3. The method of claim 1 wherein the photoresist masterlies between a first plane and a second plane, the concavities extendinto the photoresist master in the direction from the first planetowards the second plane, and the location of the maximum sag of eachconcavity relative to the first plane varies between at least someadjacent unit cells at a sufficiently slow rate so that the focusingefficiency of the microlens array is not reduced below 75 percent. 4.The method of claim 1 wherein the photoresist master lies between afirst plane and a second plane, the concavities extend into thephotoresist master in the direction from the first plane towards thesecond plane, and the distances between the apexes of the concavitiesand the first plane are different.
 5. The method of claim 4 wherein saiddistances are randomly distributed.
 6. The method of claim 5 wherein themicrolens array has a focusing efficiency of at least 75 percent.
 7. Themethod of claim 5 wherein the fill factor of the microlens array is atleast 90 percent.
 8. The method of claim 5 wherein the microlens arrayhas a focusing efficiency of at least 75 percent and a fill factor of atleast 90 percent.
 9. The method of claim 5 wherein the microlens arrayhas a focusing efficiency of at least 95 percent and a fill factorsubstantially equal to 100 percent.
 10. The method of claim 1 wherein atleast one of said concavities is anamorphic.
 11. The method of claim 1wherein the microlens array has a focusing efficiency of at least 75percent.
 12. The method of claim 1 wherein the microlens array has afocusing efficiency of at least 85 percent.
 13. The method of claim 1wherein the microlens array has a focusing efficiency of at least 95percent.
 14. The method of claim 1 wherein the fill factor of themicrolens array is at least 90 percent.
 15. The method of claim 1wherein the fill factor of the microlens array is at least 95 percent.16. The method of claim 1 wherein the fill factor of the microlens arrayis substantially equal to 100 percent.
 17. The method of claim 1 whereinthe microlens array has a focusing efficiency of at least 75 percent anda fill factor of at least 90 percent.
 18. The method of claim 1 whereinthe microlens array has a focusing efficiency of at least 95 percent anda fill factor substantially equal to 100 percent.
 19. A method forproducing a microlens array, said microlens array having a surfaceconfiguration having peaks and valleys and comprising a plurality ofunit cells and a plurality of microlenses, one microlens per unit cell,said method comprising: (a) providing a positive photoresist; (b)exposing the positive photoresist with a laser beam having a finite beamwidth at the photoresist of less than the transverse size of any of themicrolenses being formed, said exposing being performed using a directlaser writing process which employs relative movement between the finitebeam width of the laser beam and the positive photoresist to form alatent image in the photoresist; (c) developing the latent image to forma photoresist master, said photoresist master having a surfaceconfiguration which is substantially the negative of the surfaceconfiguration of the microlens array; and (d) using the photoresistmaster to: (i) produce the microlens array, and/or (ii) produce afurther master used to form the microlens array, said further masterhaving a surface configuration which is substantially the negative ofthe surface configuration of the microlens array; wherein: (A) saidmicrolens array comprises only convex microlenses at adjacent unit cellsso that the photoresist master and the further master if producedcomprises only concavities at adjacent unit cells; (B) the microlensarray has a focusing efficiency greater than 75 percent; and (C) themicrolens array would have a focusing efficiency of 75 percent or lessif prepared by the same direct laser writing process using the samelaser beam with the same finite beam width at the photoresist but withthe photoresist master being written so as to comprise convexities atadjacent unit cells rather than concavities.
 20. The method of claim 19wherein the photoresist master lies between a first plane and a secondplane, the concavities extend into the photoresist master in thedirection from the first plane towards the second plane, and thedistances between the apexes of the concavities and the first plane aredifferent.
 21. The method of claim 20 wherein said distances arerandomly distributed.
 22. The method of claim 19 wherein at least one ofsaid concavities is anamorphic.
 23. A method for producing a microlensarray, said microlens array having a surface configuration having peaksand valleys and comprising a plurality of unit cells and a plurality ofmicrolenses, one microlens per unit cell, said method comprising: (a)providing a positive photoresist; (b) exposing the positive photoresistwith a laser beam having a finite beam width at the photoresist of lessthan the transverse size of any of the microlenses being formed, saidexposing being performed using a direct laser writing process whichemploys relative movement between the finite beam width of the laserbeam and the positive photoresist to form a latent image in thephotoresist; (c) developing the latent image to form a photoresistmaster, said photoresist master having a surface configuration which issubstantially the negative of the surface configuration of the microlensarray; and of less than the transverse (d) using the photoresist masterto: (i) produce the microlens array, and/or (ii) produce a furthermaster used to form the microlens array, said further master having asurface configuration which is substantially the negative of the surfaceconfiguration of the microlens array; wherein: (A) said microlens arraycomprises only convex microlenses at adjacent unit cells so that thephotoresist master and the further master if produced comprises onlyconcavities at adjacent unit cells; (B) the microlens array has afocusing efficiency greater than 85 percent; and (C) the microlens arraywould have a focusing efficiency of 85 percent or less if prepared bythe same direct laser writing process using the same laser beam with thesame finite beam width at the photoresist but with the photoresistmaster being written so as to comprise convexities at adjacent unitcells rather than concavities.
 24. The method of claim 23 wherein thephotoresist master lies between a first plane and a second plane, theconcavities extend into the photoresist master in the direction from thefirst plane towards the second plane, and the distances between theapexes of the concavities and the first plane are different.
 25. Themethod of claim 24 wherein said distances are randomly distributed. 26.The method of claim 23 wherein at least one of said concavities isanamorphic.
 27. A method for producing a microlens array, said microlensarray having a surface configuration having peaks and valleys andcomprising a plurality of unit cells and a plurality of microlenses, onemicrolens per unit cell, said method comprising: (a) providing apositive photoresist; (b) exposing the positive photoresist with a laserbeam having a finite beam width at the photoresist of less than thetransverse size of any of the microlenses being formed, said exposingbeing performed using a direct laser writing process which employsrelative movement between the finite beam width of the laser beam andthe positive photoresist to form a latent image in the photoresist; (c)developing the latent image to form a photoresist master, saidphotoresist master having a surface configuration which is substantiallythe negative of the surface configuration of the microlens array; and(d) using the photoresist master to: (i) produce the microlens array,and/or (ii) produce a further master used to form the microlens array,said further master having a surface configuration which issubstantially the negative of the surface configuration of the microlensarray; wherein: (A) said microlens array comprises only convexmicrolenses at adjacent unit cells so that the photoresist master andthe further master if produced comprises only concavities at adjacentunit cells; (B) the microlens array has a focusing efficiency greaterthan 95 percent; and (C) the microlens array would have a focusingefficiency of 95 percent or less if prepared by the same direct laserwriting process using the same laser beam with the same finite beamwidth at the photoresist but with the photoresist master being writtenso as to comprise convexities at adjacent unit cells rather thanconcavities.
 28. The method of claim 27 wherein the photoresist masterlies between a first plane and a second plane, the concavities extendinto the photoresist master in the direction from the first planetowards the second plane, and the distances between the apexes of theconcavities and the first plane are different.
 29. The method of claim28 wherein said distances are randomly distributed.
 30. The method ofclaim 27 wherein at least one of said concavities is anamorphic.